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If u(x,y) =x^(2)y + 3xy^(4), x = e^(t) a...

If `u(x,y) =x^(2)y + 3xy^(4), x = e^(t)` and y= sin t, find `(du)/(dx)` and evaluate it at t=0.

Text Solution

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The correct Answer is:
`(dt)/(dt) = e^(0) [ 0+ 0+ 1 + 0] =1`
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Knowledge Check

  • If g(x,y) = 3x^(2) - 5y + 2y^(2), x(t) =e^(t) and y(t) = cos t , then (dg)/(dt) is equal to

    A
    `6e^(2t) + 5 sin t - 4 cos t sin t`
    B
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    C
    `3e^(2t) + 5 sin t + 4 cos t sin t`
    D
    `3e^(2t) - 5 sin t + 4 cos t sin t`

  • If g(x, y) = 3x^(2) - 5y + 2y^(2), x(t) = e^(t) and y(t) = cos t , then (dg)/(d t) is equal to

    A
    `6e^(2t) + 5 sin t - 4 cos t sin t`
    B
    `6e^(2t) - 5 sin t + 4 cos t sin t`
    C
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    D
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